Geodesic
The stability of the problem of statistical estimation and a~choice of the loss function
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 3, Tome 87 (1979), pp. 62-73

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In the article there is given the definition of the stability of the problem of statistical estimation. We prove that if the set of all symmetrical statistics form a complete class tnen the problem of statistical estimation is non-stable when the loss function of the form $W(\gamma^*,\gamma)=V(\gamma^*-\gamma)$ is used. Also there are given some examples of loss functions for which the.problem of statistical estimation is stable. 
@article{ZNSL_1979_87_a5,
     author = {L. B. Klebanov},
     title = {The stability of the problem of statistical estimation and a~choice of the loss function},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {62--73},
     publisher = {mathdoc},
     volume = {87},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_87_a5/}
}
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L. B. Klebanov. The stability of the problem of statistical estimation and a~choice of the loss function. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 3, Tome 87 (1979), pp. 62-73. http://geodesic.mathdoc.fr/item/ZNSL_1979_87_a5/